Finite Group Databasebeta

← C2×#14271669 #16832729

Subgroups — C2×#14271669 #16832729

Order 3712.

1880 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#90807C211yesmaximal, characteristic, complemented
2C24×Dic29C211yesmaximal, characteristic, complemented
3#14271669C2116yesmaximal, direct product factor
4C2×#11745248C211yesmaximal, characteristic, complemented
5C2×#11745297C211yesmaximal, characteristic, complemented
6C2×#11745240C212yesmaximal, complemented
7C2×#11745301C212yesmaximal, complemented
8C2×#11745315C211yesmaximal, characteristic, complemented
9C2×D4×Dic29C212yesmaximal, complemented
10C2×#11745243C212yesmaximal, complemented
11C2×#11745239C211yesmaximal, characteristic, complemented
12C2×C29×#120C211yesmaximal, characteristic, complemented
13C25×C29C2211yescharacteristic
14C22×D4×C29C2212yes—
15C22×D4×C29C2211yescharacteristic
16C22×C22⋊D29C2212yes—
17C22×C22⋊D29C2211yescharacteristic
18C22×C22⋊D29C2211yescharacteristic, complemented
19C23×Dic29—28no—
20C23×Dic29C2212yes—
21C23×Dic29C2212yes—
22C23×Dic29C2211yescharacteristic
23C23×Dic29C2211yescharacteristic
24C23×Dic29C2218yescomplemented
25C23×Dic29C2211yescharacteristic, complemented
26C2×#90807—28no—
27C2×#90807C2218yescomplemented
28C22×C4×D29C2211yescharacteristic, complemented
29C22×Dic58C2211yescharacteristic, complemented
30C29×#120C2218yescomplemented
31C2×C22⋊C4×C29C2211yescharacteristic
32C2×C22⋊C4×C29C2212yes—
33#11745315C2218yescomplemented
34C2×C22⋊Dic29C2211yescharacteristic
35C2×C22⋊Dic29C2212yes—
36C2×C22⋊Dic29C2212yescomplemented
37#11745301C22116yescomplemented
38#11745297C2218yescomplemented
39D4×Dic29C22116yescomplemented
40C2×#90781C2212yescomplemented
41C2×C4⋊Dic29C2212yescomplemented
42C2×#90779C2212yescomplemented
43C2×#90779C2212yescomplemented
44C2×C4×Dic29C2212yescomplemented
45#11745248C2218yescomplemented
46#11745243C22116yescomplemented
47#11745240C22116yescomplemented
48#11745239C2218yescomplemented
49C24×C29—24no—
50C24×C29—28no—
51C24×C29C2311yescharacteristic
52C24×C29C2314yes—
53C24×C29C2311yescharacteristic
54C24×C29C2312yes—
55C23×D29C2311yescharacteristic
56C2×D4×C29—24no—
57C2×D4×C29—28no—
58C2×D4×C29C2318yes—
59C2×D4×C29C2314yes—
60C22×C4×C29C2312yes—
61C22×C4×C29C2311yescharacteristic
62C2×C22⋊D29—24no—
63C2×C22⋊D29—28no—
64C2×C22⋊D29—24no—
65C2×C22⋊D29C2318yes—
66C2×C22⋊D29C2314yes—
67C2×C22⋊D29C2314yescomplemented
68C22×Dic29—24no—
69C22×Dic29—24no—
70C22×Dic29—28no—
71C22×Dic29—28no—
72C22×Dic29—232no—
73C22×Dic29D418yescomplemented
74C22×Dic29C2312yes—
75C22×Dic29C2312yes—
76C22×Dic29C2311yescharacteristic
77C22×Dic29C2318yes—
78C22×Dic29C2314yes—
79C22×Dic29C2318yes—
80C22×Dic29C2311yescharacteristic
81C22×Dic29C2311yescharacteristic
82C22×Dic29C2314yes—
83C22×Dic29C2314yescomplemented
84#90807—232no—
85C2×C4×D29—24no—
86C2×C4×D29C2314yescomplemented
87C2×Dic58—24no—
88C2×Dic58C2314yescomplemented
89C22⋊C4×C29C2314yes—
90C22⋊C4×C29C2318yes—
91C22⋊Dic29C2318yes—
92C22⋊Dic29C2314yes—
93C22⋊Dic29C2318yescomplemented
94#90781C2318yescomplemented
95C4⋊Dic29C2318yescomplemented
96#90779C2318yescomplemented
97#90779C2318yescomplemented
98C4×Dic29C2318yescomplemented
99C23×C29—232no—
100C23×C29—28no—
101C23×C29—24no—
102C23×C29—24no—
103C23×C29—24no—
104C23×C29—216no—
105C23×C29—22no—
106C23×C29—24no—
107C23×C29C2×D414yes—
108C23×C29#4118yescomplemented
109C23×C29C2412yes—
110C23×C29C2412yes—
111C23×C29C2414yes—
112C23×C29C2411yescharacteristic
113C22×D29—22no—
114C22×D29—24no—
115C22×D29C2412yes—
116D4×C29—28no—
117D4×C29—216no—
118C2×C4×C29—22no—
119C2×C4×C29—24no—
120C2×C4×C29C2414yes—
121C2×C4×C29C2412yes—
122C22⋊D29—28no—
123C22⋊D29—216no—
124C22⋊D29—28no—
125C2×Dic29—22no—
126C2×Dic29—28no—
127C2×Dic29—24no—
128C2×Dic29—24no—
129C2×Dic29—28no—
130C2×Dic29—216no—
131C2×Dic29—216no—
132C2×Dic29C2×D414yes—
133C2×Dic29C2×D414yes—
134C2×Dic29C2×D4116yescomplemented
135C2×Dic29C2414yes—
136C2×Dic29C2414yes—
137C2×Dic29C2412yes—
138C2×Dic29C2412yes—
139C2×Dic29C2412yes—
140C4×D29—28no—
141Dic58—28no—
142C2×#525—291nomaximal, Sylow
143C22×C29—232no—
144C22×C29—28no—
145C22×C29—216no—
146C22×C29—24no—
147C22×C29—24no—
148C22×C29—24no—
149C22×C29—22no—
150C22×C29—24no—
151C22×C29—44no—
152C22×C29C22×D414yes—
153C22×C29C22×D412yes—
154C22×C29C2×#4114yes—
155C22×C29C2×#4118yescomplemented
156C22×C29C2511yescharacteristic
157C2×D29—22no—
158C2×D29—24no—
159C2×D29—44no—
160C4×C29—22no—
161C4×C29—24no—
162Dic29—22no—
163Dic29—24no—
164Dic29—24no—
165Dic29C22×D414yes—
166Dic29C22×D414yes—
167C22×#41—291no—
168C24×C4—291no—
169#525—2916no—
170C2×#123—291no—
171C2×#123—291no—
172C2×C22⋊Q8—292no—
173C2×#121—292no—
174C2×#120—291no—
175C2×#120D2911yescharacteristic, complemented
176C2×C4×D4—292no—
177C2×C4×D4—292no—
178C2×#117—291no—
179C2×C29—24no—
180C2×C29—28no—
181C2×C29—42no—
182C2×C29#52514yescomplemented
183C2×C29C23×D411yescharacteristic
184C2×C29C22×#4112yes—
185D29—42no—
186C25C2×D2911yescharacteristic
187C2×#41—298no—
188C2×#41—588no—
189C22×Q8—291no—
190C22×D4—292no—
191C22×D4—291no—
192C22×D4—291no—
193C22×D4C2×D2912yes—
194C22×D4C2×D2911yescharacteristic
195C23×C4—291no—
196C23×C4—292no—
197C23×C4—291no—
198C23×C4—292no—
199C23×C4—291no—
200C23×C4—298no—
201C23×C4—291no—
202C23×C4—588no—
203#123—298no—
204#123—298no—
205C22⋊Q8—2916no—
206#121—2916no—
207#120—298no—
208#120C2×D2918yescomplemented
209C4×D4—2916no—
210C4×D4—2916no—
211#117—298no—
212C2×C4⋊C4—292no—
213C2×C4⋊C4—292no—
214C2×C4⋊C4—292no—
215C2×C22⋊C4—291no—
216C2×C22⋊C4—292no—
217C2×C22⋊C4—292no—
218C2×C22⋊C4—292no—
219C2×C22⋊C4C2×D2911yescharacteristic
220C2×C22⋊C4C2×D2912yes—
221C2×C42—292no—
222C29C2×#52511yescharacteristic, complemented, Sylow
223C24—24no—
224C24—28no—
225C24—291no—
226C24C22×D2914yes—
227C24C22×D2911yescharacteristic
228C24C22×D2911yescharacteristic
229C24C22×D2912yes—
230#41—5832no—
231C2×Q8—294no—
232C2×Q8—584no—
233C2×D4—24no—
234C2×D4—28no—
235C2×D4—298no—
236C2×D4—294no—
237C2×D4—294no—
238C2×D4—584no—
239C2×D4—584no—
240C2×D4—588no—
241C2×D4C22×D2918yes—
242C2×D4C22×D2914yes—
243C22×C4—298no—
244C22×C4—294no—
245C22×C4—291no—
246C22×C4—291no—
247C22×C4—298no—
248C22×C4—294no—
249C22×C4—298no—
250C22×C4—294no—
251C22×C4—292no—
252C22×C4—292no—
253C22×C4—291no—
254C22×C4—294no—
255C22×C4—584no—
256C22×C4—588no—
257C22×C4—588no—
258C22×C4—5832no—
259C22×C4—584no—
260C22×C4—584no—
261C22×C4C22×D2912yes—
262C22×C4C22×D2911yescharacteristic
263C4⋊C4—298no—
264C4⋊C4—298no—
265C4⋊C4—298no—
266C22⋊C4—294no—
267C22⋊C4—298no—
268C22⋊C4—298no—
269C22⋊C4—298no—
270C22⋊C4C22×D2914yes—
271C22⋊C4C22×D2918yes—
272C42—298no—
273C23—232no—
274C23—28no—
275C23—24no—
276C23—24no—
277C23—24no—
278C23—216no—
279C23—22no—
280C23—24no—
281C23—292no—
282C23—582no—
283C23—584no—
284C23D4×D2914yes—
285C23#9080718yescomplemented
286C23C23×D2912yes—
287C23C23×D2912yes—
288C23C23×D2914yes—
289C23C23×D2911yescharacteristic
290Q8—588no—
291D4—28no—
292D4—216no—
293D4—588no—
294D4—588no—
295D4—5816no—
296C2×C4—22no—
297C2×C4—24no—
298C2×C4—294no—
299C2×C4—294no—
300C2×C4—2916no—
301C2×C4—292no—
302C2×C4—292no—
303C2×C4—294no—
304C2×C4—294no—
305C2×C4—292no—
306C2×C4—588no—
307C2×C4—5816no—
308C2×C4—5816no—
309C2×C4—588no—
310C2×C4—588no—
311C2×C4—584no—
312C2×C4—582no—
313C2×C4—584no—
314C2×C4C23×D2914yes—
315C2×C4C23×D2912yes—
316C22—232no—
317C22—28no—
318C22—216no—
319C22—24no—
320C22—24no—
321C22—24no—
322C22—22no—
323C22—24no—
324C22—44no—
325C22—582no—
326C22—584no—
327C22—1164no—
328C22C2×D4×D2914yes—
329C22C2×D4×D2912yes—
330C22C2×#9080714yes—
331C22C2×#9080718yescomplemented
332C22C24×D2911yescharacteristic
333C4—22no—
334C4—24no—
335C4—294no—
336C4—294no—
337C4—584no—
338C4—582no—
339C4—584no—
340C2—24no—
341C2—28no—
342C2—42no—
343C2—1162no—
344C2#1427166914yesdirect product factor
345C2C22×D4×D2911yescharacteristic
346C2C22×#9080712yes—
subgroupG/H
centerC23C23×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC2×C29×#120C2
socleC23×C29C24
hypercenterC2×#120D29
hypocenterC29C2×#525
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×#120

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#90807C2semidirect
2. C24×Dic29C2semidirect
3. #14271669C2direct (N × H)
4. C2×#11745248C2semidirect
5. C2×#11745297C2semidirect
6. C2×#11745240C2semidirect
7. C2×#11745301C2semidirect
8. C2×#11745315C2semidirect
9. C2×D4×Dic29C2semidirect
10. C2×#11745243C2semidirect
11. C2×#11745239C2semidirect
12. C2×C29×#120C2semidirect
18. C22×C22⋊D29C22semidirect
24. C23×Dic29C22semidirect
25. C23×Dic29C22semidirect
27. C2×#90807C22semidirect
28. C22×C4×D29C22semidirect
29. C22×Dic58C22semidirect
30. C29×#120C22semidirect
33. #11745315C22semidirect
36. C2×C22⋊Dic29C22semidirect
37. #11745301C22semidirect
38. #11745297C22semidirect
39. D4×Dic29C22semidirect
40. C2×#90781C22semidirect
41. C2×C4⋊Dic29C22semidirect
42. C2×#90779C22semidirect
43. C2×#90779C22semidirect
44. C2×C4×Dic29C22semidirect
45. #11745248C22semidirect
46. #11745243C22semidirect
47. #11745240C22semidirect
48. #11745239C22semidirect
67. C2×C22⋊D29C23semidirect
73. C22×Dic29D4semidirect
83. C22×Dic29C23semidirect
86. C2×C4×D29C23semidirect
88. C2×Dic58C23semidirect
93. C22⋊Dic29C23semidirect
94. #90781C23semidirect
95. C4⋊Dic29C23semidirect
96. #90779C23semidirect
97. #90779C23semidirect
98. C4×Dic29C23semidirect
108. C23×C29#41semidirect
134. C2×Dic29C2×D4semidirect
155. C22×C29C2×#41semidirect
175. C2×#120D29semidirect
182. C2×C29#525semidirect
208. #120C2×D29semidirect
222. C29C2×#525semidirect
285. C23#90807semidirect
331. C22C2×#90807semidirect
344. C2#14271669direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#908072
C24×Dic292
#142716692
C2×#117452482
C2×#117452972
C2×#117452402
C2×#117453012
C2×#117453152
C2×D4×Dic292
C2×#117452432
C2×#117452392
C2×C29×#1202
C2×#52529